24 As Dr Bonnie J. Blackburn (pers. comm.) points out, instead of dividing the string by ratios and sounding the longer part, Maas took for model one of the three instruments he mentions, namely the guitar, on whose fingerboard the semitones are separated by frets. The note sounded at the fifth fret, which divides the whole string in 1/4 and 3/4, yields the perfect fourth; the next seven frets, which occupy the same space on the fingerboard and in Maas's diagram as the first five, cover the adjoining fifth, reaching to the mid-point of the string, which yields the octave.

* I wish to thank Bonnie Blackburn, K. M. Coleman, and Franco Cavazza for helpful comments and information; Albinia de la Mare for making available her microfilm of the Cesena MS. (n. 17); Nigel Wilson for bringing the Lincoln incunable of Gellius to my attention; and the Librarian, Fiona Piddock, for assistance in identifying the donor.